Abstract
In the previous papers(13, 14, 15), I introduced new stress rate, namely, linear stress rate in order to formulate nonlinear beam element. This stress rate is non-symmetric, but its material stiffness matrix holds symmetry. Then, it has only the geometric stiffness of rigid rotation as the geometric stiffness. Because the study of the strain and the constitutive equation for this stress rate is necessary, I will show that the stress rate is consistent with linear strain, which is linear about the right stretch tensor, and that the constitutive equation consists of the linear strain and the transpose of the first Piola-Kirchhoff stress. Then, the simple shear problem will be shown to consider this strain.
